What is the derivative of log_{e}(3x) ?

The derivative of log_{e}(3x) is 1/x

What is the first derivative of log_{e}(3x) ?

The first derivative of log_{e}(3x) is 1/x

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\frac{d}{d x} (lo g_{e} (3 x))

\frac{1}{x}

Solution steps

\frac{d}{d x} (lo g_{e} (3 x))

Simplify

lo g_{e} (3 x) : ln (3 x)

= \frac{d}{d x} (ln (3 x))

Apply the chain rule:

\frac{1}{3 x} \frac{d}{d x} (3 x)

= \frac{1}{3 x} \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = 3

= \frac{1}{3 x} \cdot 3

Simplify

\frac{1}{3 x} \cdot 3 : \frac{1}{x}

= \frac{1}{x}

What is the derivative of log_{e}(3x) ?
The derivative of log_{e}(3x) is 1/x
What is the first derivative of log_{e}(3x) ?
The first derivative of log_{e}(3x) is 1/x